Markov Trace on the Yokonuma–hecke Algebra

Abstract

It is proved that the Yokonuma-Hecke algebra supports a Markov trace.

The Yokonuma–hecke Algebras and the Homflypt Polynomial

“…It is easily verified that the elements e i are idempotents in Y d,n (u) [Ju,Lemma 4]. Also, that the elements g i are invertible, with (2.4) g…”

Determination of the Representations and a Basis for the Yokonuma–Temperley–Lieb Algebra

“…Juyumaya [Ju2] has shown that the following set is a basis for the Yokonuma-Hecke algebra Y d,n (u):…”

“…, t n are the generators of (Z/dZ) n (recall that Y d,n (u) is a quotient of (Z/dZ) n ⋊ B n ). Juyumaya [Ju2] has shown that, starting with the standard basis B IH of the Iwahori-Hecke algebra H n (u) (case d = 1), one can obtain naturally a basis B YH for the Yokonuma-Hecke algebra Y d,n (u) in the following way:…”

Skein Invariants of Links and Their State Sum Models

“…Note that in the transition from (13) to (14) the partition set π changes from all partitions of L to only partitions of L for which L 1 and L 2 are in different subsets. The equality in (14) follows from the equality in (13) once this difference in partitions is appreciated. Hence, using (14) and also (12), we obtain:…”

“…The equality in (14) follows from the equality in (13) once this difference in partitions is appreciated. Hence, using (14) and also (12), we obtain:…”